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Chapter 27
Magnetism
27-4 Force on an Electric Charge
Moving in a Magnetic Field
The force on a moving charge is related
to the force on a current:
Once again, the direction is given
by a right-hand rule.
Magnetic Force
on a point charge
Force on a moving charge
(
F = q v´B
)
Direction: Right hand rule
F is Perpendicular to both v and
Lay hand along v palm toward B
+q  Thumb points along F
-q  Thumb points opposite F
= out of page
Arrow coming at you
B
B
= into page
Arrow leaving you
v
F
Magnetic Force
on a point charge
Direction: RIGHT Hand Rule
Perpendicular to both v and B
Here Into
or Out of
the page
Run fingers along v, curl them towards B,
•If q is positive, thumb points along F
•If q is negative, thumb points opposite F
Magnetic Force
on a point charge
• If q is + find the
direction of F
F
v
B
F
B
F
v
B
v
Problem 17
• 17.(I) Determine the direction of for each case in
Fig. 27–43, where represents the maximum
magnetic force on a positively charged particle
moving with velocity
27-4 Force on an Electric Charge
Moving in a Magnetic Field
Example 27-5: Magnetic force on a proton.
A magnetic field exerts a force of 8.0 x 10-14 N toward the
west on a proton moving vertically upward at a speed of 5.0 x
106 m/s . When the proton is moving horizontally in a northerly
direction, the force on it is zero . Determine the magnitude
and direction of the magnetic field in this region. (The charge
on a proton is q = +e = 1.6 x 10-19 C.)
27-4 Force on an Electric Charge
Moving in a Magnetic Field
If a charged particle is moving
(electron) perpendicular to a
uniform magnetic field, its path
will be a circle.
What if you have a proton?
27-4 Force on an Electric Charge
Moving in a Magnetic Field
Example 27-7: Electron’s path in a uniform magnetic
field.
An electron travels at 2.0 x 107 m/s in a plane
perpendicular to a uniform 0.010-T magnetic field.
Describe its path quantitatively.
27-4 Force on an Electric Charge
Moving in a Magnetic Field
Problem solving: Magnetic fields – things to
remember:
1.The magnetic force is perpendicular to the
magnetic field direction.
2.The right-hand rule is useful for determining
directions. The right-hand rule gives the
direction.
3.Equations in this chapter give magnitudes
only.
27-4 Force on an Electric Charge
Moving in a Magnetic Field
Charged particles in B-fields
•
•
•
Aurora Borealis: Northern Lights
Aurora Australis: Southern Lights
Due to ions (e- & p+) from the Sun
–
Travel from Sun to Earth in ~ 3 days
• 93 million miles in 3 days ~ 30 million miles/day
www.spaceweather.com
Aurora on
11/20/03,
Zagreb,
Croatia.
Photo by
Hrvoje
Horvat
http://www.nasa.gov/mpg/143772main_SolarCycleCME_Reconnection.mpg
Aurora
Ions steered to poles by Earth’s mag. field
– Collide with molecules in atmosphere
• ionize particles, recombination produces light:
Aurora
– More energetic particles get closer to Earth
http://www.swpc.noaa.gov/pmap/
Lorentz Equation
Mass Spectrometer
v =
E1
B1
r=
For selected speeds
mv
qB
æ
ö
E
m
1
r=
ç ÷
qB çè B1 ÷ø
Electromagnetic Flowmeter
+ v
-
- - - - - - B
d
E
+ + + + + + +
B
∆V
A flowmeter read the blood flow in
organs, and determine the oxygen
flow, nutrients, hormones and so on,
and is connected to the body
through a catheter and a voltage is
applied.
Charges build until forces balance!
FE = FB
qE = qvB
v flow =
E
B
=
DV
Bd
We know B since we applied it.
E is determined from V and the
width of the artery d
E=V/d
27-4 Force on an Electric Charge
Moving in a Magnetic Field
Conceptual Example 27-10: Velocity selector, or
filter: crossed B
E and E
B fields.
Some electronic devices and experiments need a beam
of charged particles all moving at nearly the same
velocity. This can be achieved using both a uniform
electric field and a uniform magnetic field, arranged
so they are at right angles to each other. Particles of
charge q pass through slit S1 and enter the region
where BB points into the page and E
E points down from
the positive plate toward the negative plate. If the
particles enter with different velocities, show how
this device “selects” a particular velocity, and
determine what this velocity is.
Problem 25